7.
The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { l l } 2 & 0
0 & 1 \end{array} \right)\).
- Find \(\mathbf { A } ^ { 2 }\) and \(\mathbf { A } ^ { 3 }\).
- Hence suggest a suitable form for the matrix \(\mathbf { A } ^ { n }\).
- Use induction to prove that your answer to part (ii) is correct.